Like with every other Pokémon Mystery Dungeon game, outside of the story there are a variety of missions to complete. These missions are randomly generated using different Pokémon, items and dungeons, and will regenerate after the completion of any mission. Should you fail the mission, Azumarill will store it for you be able to retry later. It can store up to 16 missions and if all 16 slots are filled, you can't complete others until space has been cleared up.
Each mission has a difficulty level from 1 star up to 10 stars and offers prizes upon completion including items, seeds and materials to build up the Pokémon Paradise. They'll also increase the rank points of the Pokémon Paradise itself. Once it reaches a certain rank,stronger missions start to get added

Standard Missions

Modes Available
Standard Mode
Friend Mode

Description:
These missions are the standard missions you have been accustomed to in the previous Mystery Dungeon games. In them, you're given a specific task in a dungeon. This is on a specific floor in the dungeon. The types of mission are as follows

Rescue - Go into the dungeon to rescue a Pokémon. This is also how StreetPass missions work

Item Retrieval - A Pokémon has lost their item in a dungeon. They task you with the job of finding it. The item will sparkle when you see it so you know it's not a standard item

Unruly Pokémon - You get informed that a specific Pokémon is causing havoc in the dungeon. You get sent to defeat and retrieve it

After defeating the game, when you get your Pokémon Paradise rank up to Ultra, missions involving Legendary Pokémon start appearing. These missions typically end with the Legendary Pokémon joining your squad

Special Missions

Modes Available
Standard Mode (Post-Ending)
Friend Mode
Local Play

Description:
The special missions are a new type of mission only accessible in Friend Mode or when in local play. These missions are fairly basic, but have good rewards. You can only take one Pokémon of yours into the mission so you need to plan accordingly.

Group - In this mode, you get challenged to a face off of a gang of Pokémon. You have to defeat all four Pokémon in order to win the mission. The types of Pokémon vary and, as difficulty increases,

Legendary battle - In this mode, you get to face off against Legendary Pokémon: Reshiram, Zekrom, Kyurem (all forms), Lugia and Ho-Oh. These battles are akin to the battle against Kyurem in the story, and have many special move animations. You cannot recruit the Pokémon.

With the Legendary Pokémon, you may go in to the battle and notice that the Pokémon you are facing are actually shiny. When they're shiny, they have slightly different moves and higher stats.